Dollar General said Thursday that it won’t back off its attempt to buy Family Dollar, after the Matthews-based retailer rejected its bid and stuck with plans to be acquired by Dollar Tree.

The swift rejection, coming just four days after Dollar General announced its unsolicited bid to acquire Family Dollar for $9.7 billion, sets up a fight for one of the Charlotte region’s best-known companies, one that employs about 1,400 workers at its Matthews headquarters.

Family Dollar’s board of directors voted unanimously to reject Dollar General’s all-cash offer of $78.50 a share. Even though the offer was higher than Dollar Tree’s $74.50 cash-and-stock bid, the board cited the risk of antitrust regulators blocking a Dollar General-Family Dollar combination.

Some analysts predicted Dollar General would come back with a higher offer. But a person familiar with the Family Dollar board’s deliberations said board members believe antitrust regulators would reject the deal if the combined company sold only 700 stores. That’s how many Dollar General has said it’s willing to sell to win approval.

That means that a higher offer alone from Dollar General likely wouldn’t sway board members, who wouldn’t want to risk dropping the Dollar Tree deal only to see a Dollar General acquisition blocked and shareholders left with nothing. Dollar Tree and Family Dollar have already begun the antitrust review process with government officials, the person said.

The jockeying for Family Dollar turned acrimonious this week, with the companies sending out dueling statements and accusing each other of misrepresenting the facts. The war of words was an extraordinary escalation in the contest for a company founded in Charlotte in 1959.

Family Dollar chief executive Howard Levine said in a statement Thursday that the company had reviewed Dollar General’s offer and concluded the antitrust issues are too great to overcome. The combined company would have many overlapping locations and would be more than three times bigger than Dollar Tree, its next-largest rival.

Levine, son of company founder Leon Levine, also struck back at a public letter Dollar General’s CEO sent to Family Dollar’s board late Wednesday. Rick Dreiling wrote that Levine ignored previous offers from Dollar General in order to find a deal where Howard Levine could keep his job at the combined company, which the Dollar Tree deal lets him do. Dreiling also said Levine and Family Dollar misled him about whether the company was really for sale, and unfairly favored Dollar Tree.

“Dollar General’s letter, sent late last night, contained blatant mischaracterizations and did nothing to address the antitrust issues in Dollar General’s proposal,” Levine said.

Family Dollar’s board agreed to accept Virginia-based Dollar Tree’s offer in July. The company had been exploring a sale for months, as it struggled to boost results and catch up with more profitable rivals. Prominent activist investor Carl Icahn was also publicly agitating for Family Dollar to be sold.

But Tennessee-based Dollar General threw the deal into question on Monday, when the company first announced its bid.

Dreiling said in a statement Thursday that his company is still committed to acquiring Family Dollar. He didn’t say whether Dollar General is planning to raise its offer or pursue other avenues, such as going directly to shareholders to block the Dollar Tree deal.

Dollar General, Family Dollar and Dollar Tree are the No. 1, No. 2 and No. 3 companies in the dollar store market, respectively. They’ve grown rapidly, expanding as they cater to customers who continue to struggle in the aftermath of the recession.

A combined Dollar General-Family Dollar would have $28 billion in revenue and almost 20,000 stores, making it by far the largest small-box discount retailer in the nation.

A Dollar Tree-Family Dollar combination would have $18 billion worth of revenue and 13,000 stores. Since Dollar General operates about 11,500 stores, that would still make a combined Dollar Tree-Family Dollar the largest discount retailer – but by a far smaller margin.

Federal regulators are likely to look closely at any such deal. Although Dollar General executives have insisted selling 700 stores would be enough to satisfy regulators, Family Dollar board member Ed Garden said the risk of being blocked by antitrust regulators is too high.

“Given the significant antitrust issues involved with Dollar General’s proposal, we will not jeopardize the Dollar Tree deal for a transaction with Dollar General that has a high likelihood of not closing,” said Garden, a partner in Trian Fund Management, in a statement.

Rahul Sharma, managing director of Neev Capital, said he doesn’t believe antitrust regulators would scuttle the deal. A combined Dollar General-Family Dollar would still be small compared to companies that have hundreds of billions worth of sales, such as Wal-Mart Stores and Kroger, with whom they would compete for grocery and consumable sales.

“An antitrust argument just doesn’t make sense,” said Sharma. He warned not to expect Dollar General to go away quietly.

“Dollar General is so in the driver’s seat here. They’ve got so much left in the war chest,” said Sharma. He estimated that while Dollar Tree is already close to its maximum bid at $74.50 a share, Dollar General could afford to go several dollars higher than its own $78.50 bid.

He said Levine’s role in the combined company – or lack thereof – could be a real sticking point. “His family were the founders of this business, and people don’t like to let that go,” said Sharma.

But Garden’s support for the Dollar Tree deal could undercut the accusation that Levine’s ambition or the board’s loyalty to its CEO played a role in rejecting Dollar General. Trian, Garden’s fund, is led by activist investor Nelson Peltz. Garden and Peltz were part of the original activist investor fund that pressured Family Dollar to sell the company starting in 2010, and they have clashed with Levine in the past.

Family Dollar hasn’t set a date for shareholders to vote on the Dollar Tree deal. The company’s two biggest shareholders – Levine, who controls 8.2 percent of Family Dollar’s stock, and Trian, with 7.3 percent – have committed to vote for Dollar Tree.

Dollar Tree has said it would keep the Family Dollar name and many of the company’s 1,400 corporate jobs in Matthews. Levine would remain with the combined company for at least two years, and would join the Dollar Tree board.

Dollar General hasn’t said what it would do with Family Dollar’s Matthews headquarters or the company name, or what Levine’s role would be. Some analysts have said that since Dollar General and Family Dollar have such similar business plans, such a deal would likely mean deep cuts in Matthews. Staff writer Eric Frazier contributed.